To find the velocity of the center of mass, we can use the principle of conservation of momentum. The total momentum of the system before the interaction is equal to the total momentum after the interaction.
The momentum of an object is given by the product of its mass and velocity (p = mv). Let's denote the masses of the two bodies as m1 and m2, and their velocities as v1 and v2, respectively. The center of mass velocity (Vcm) can be calculated as follows:
Total initial momentum = Total final momentum
(m1 * v1) + (m2 * v2) = (m1 + m2) * Vcm
Substituting the given values:
(2 kg * 2 m/s) + (4 kg * (-10 m/s)) = (2 kg + 4 kg) * Vcm
4 kg·m/s - 40 kg·m/s = 6 kg * Vcm
-36 kg·m/s = 6 kg * Vcm
Dividing both sides by 6 kg:
Vcm = -6 m/s
Therefore, the velocity of the center of mass is -6 m/s, indicating that it is moving in the opposite direction of the bodies' initial velocities.